88.4.6 problem 6

Internal problem ID [23970]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 33
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:48:08 PM
CAS classification : [_separable]

\begin{align*} \cos \left (x \right ) \cot \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 10

ode:=cos(x)*cot(y(x))+sin(x)*cos(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arccos \left (\ln \left (\sin \left (x \right )\right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.311 (sec). Leaf size: 101

ode=Cos[x]*Cot[y[x]]+Sin[x]*Cos[y[x]]*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {3 \pi }{2}\\ y(x)&\to -\frac {\pi }{2}\\ y(x)&\to \frac {\pi }{2}\\ y(x)&\to \frac {3 \pi }{2}\\ y(x)&\to -\arccos (\log (\sin (x))-c_1)\\ y(x)&\to \arccos (\log (\sin (x))-c_1)\\ y(x)&\to -\frac {3 \pi }{2}\\ y(x)&\to -\frac {\pi }{2}\\ y(x)&\to \frac {\pi }{2}\\ y(x)&\to \frac {3 \pi }{2} \end{align*}

✓ Sympy. Time used: 0.320 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sin(x)*cos(y(x))*Derivative(y(x), x) + cos(x)*cot(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \operatorname {acos}{\left (C_{1} + \log {\left (\sin {\left (x \right )} \right )} \right )} + 2 \pi , \ y{\left (x \right )} = \operatorname {acos}{\left (C_{1} + \log {\left (\sin {\left (x \right )} \right )} \right )}\right ] \]